Question

1. [20] A small building that shelters a water supply pump measures 2 m ×3 m ×2.4 m high. It is constructed of 1-cm thick wood having a thermal conductivity of 0.126 W∙m-1 ∙K -1 . The inside walls are to be maintained at 10 oC when the outside temperature is -18 oC. How much heat must be supplied to maintain the desired temperature? How much heat must be supplied if the walls are lined with 10 cm of glass-wool insulation having a thermal conductivity of 0.0377 W∙m-1 ∙K - 1 ? Assume there is no heat loss through the floor. Ignore the wood in the second calculation.

Answer 1

area of top panel = 2 x 3 = 6 m^2

area of side panel = 2 (2 x 2.4) = 9.6 m^2

area of side panel = 2 (3 x 2.4) = 14.4 m^2

total area = 6 + 9.6 + 14.4 = 30.0 m^2

temperature of out side = - 18 + 273 = 255 K

inside temperature = 10 + 273 = 283 K

temperature difference dT = 283 - 255 = 28 0C

heat q = k A x dT / dx

          = 0.126 x 30 x 28 / 0.01

          = 10584 W

heat must be supplied to maintain the desired temperature = 10584 W

heat when glass wool insulation :

q = 0.0377 x 30 x 28 / 0.1

    = 316.68 W